Gael García Bernal Caught Up in Paternity Drama

Gael García Bernal's latest role? Starring in a slew of online rumors claiming that he split from his girlfriend and may not have actually fathered his 1-year-old son, Lázaro. But sources tell PEOPLE there's no truth to the accusations.

"It's completely untrue," says a source close to the actor, adding that Bernal and his girlfriend, Argentine actress Dolores Fonzi, "are happy together and they love their son. This is totally made up."

Several blogs reported this week that the Babel and Motorcycle Diaries actor, 31, and Fonzi called it quits. And, in a telenovela-like twist, there's chatter that Bernal is demanding a DNA test for his Lázaro after hearing that Fonzi, also 31, may have been unfaithful.

A rep for Bernal confirms that the online rumors are false. A rep for Fonzi had no comment.

Last year, Bernal's Blindness director Fernando Meirelle told PEOPLE the Mexican actor was "so excited" when he learned he'd be a dad. "He's really looking forward to it."